We compare two methods of motivating money in New Keynesian dynamic stochastic general equilibrium models - money-in-the-utility function and the cash-in-advance (CIA) constraint - as well as two ways of modelling monetary policy: the interest rate feedback rule and money growth rules. As an aid to model selection, we use a new econometric measure of the distance between model and data variance-covariance matrices. The proposed measure is useful in distinguishing between alternative general equilibrium models. Drawing on our econometric analysis, we argue that the CIA model, closed by a money growth rule, comes closest to the data. © 2007 Blackwell Publishing Ltd and The University of Manchester.